Question: Solve for $x$ and $y$ using elimination. ${-2x-y = -24}$ ${5x+y = 45}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $3x = 21$ $\dfrac{3x}{{3}} = \dfrac{21}{{3}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-2x-y = -24}\thinspace$ to find $y$ ${-2}{(7)}{ - y = -24}$ $-14-y = -24$ $-14{+14} - y = -24{+14}$ $-y = -10$ $\dfrac{-y}{{-1}} = \dfrac{-10}{{-1}}$ ${y = 10}$ You can also plug ${x = 7}$ into $\thinspace {5x+y = 45}\thinspace$ and get the same answer for $y$ : ${5}{(7)}{ + y = 45}$ ${y = 10}$